Sparse Recovery Using Modified SL0 Algorithm by Weighted Projection and Application to ISAR Imaging

Sparse recovery is widely used in various fields where Compressed Sensing (CS) is one of the most popular. Recently, researchers have made a lot of effort to reduce Inverse Synthetic Aperture Radar (ISAR) imaging costs using the CS. One method for solving sparse recovery problem is Smoothed L0 norm (SL0), in which the aim is to approximate the L0 norm with a convex function and minimize it in such a way that the feasible region constraint is satisfied. In this paper, we present the Modified SL0 algorithm (MSL0) by changing the projection stage of the SL0 and performing it as weighted. By adding a weighing matrix to the projection stage, a more sparse solution with higher recovery quality is achieved using MSL0 compared to the SL0. Regarding the results of numerical experiments, the recovery SNR for the new algorithm compared to the original SL0, under the same test conditions, was about 10 dB higher. In another part of the paper, the formulation of ISAR imaging based on a Scattering Point Model of targets and the use of the CS to reconstruct undersampled ISAR images are rewritten. Using an experiment, the efficiency of the MSL0 is evaluated for the reconstruction of ISAR images. In the experiment, ISAR imaging is applied on a radar data from a B727 airplane is used to create an ISAR image, in which in which the samples recorded in each range bin can be assumed to be sparse. The results of this simulation indicate that the quality of image reconstruction with MSL0 is better than SL0 and IFFT with least energy for various compression rates.